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<a href="_n_s_g_a3_indicator_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       Algorithm selecting front based on their crowding distance</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> *</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * \author      O.Krause</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * \date        2017</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> *</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> *</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> *</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> *</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> */</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_DIRECTSEARCH_INDICATORS_NSGA3_INDICATOR_H</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="preprocessor">#define SHARK_ALGORITHMS_DIRECTSEARCH_INDICATORS_NSGA3_INDICATOR_H</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#include &lt;<a class="code" href="_base_8h.html">shark/LinAlg/Base.h</a>&gt;</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#include &lt;<a class="code" href="_key_value_pair_8h.html">shark/Core/utility/KeyValuePair.h</a>&gt;</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &lt;<a class="code" href="_lattice_8h.html">shark/Algorithms/DirectSearch/Operators/Lattice.h</a>&gt;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
<div class="foldopen" id="foldopen00043" data-start="{" data-end="};">
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="structshark_1_1_n_s_g_a3_indicator.html">   43</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_n_s_g_a3_indicator.html">NSGA3Indicator</a> {</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ParetofrontType, <span class="keyword">typename</span> ParetoArchive&gt;</div>
<div class="foldopen" id="foldopen00045" data-start="{" data-end="}">
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="structshark_1_1_n_s_g_a3_indicator.html#ae2a8e94c8556e915e1c7e306159a432b">   45</a></span>    std::vector&lt;std::size_t&gt; <a class="code hl_function" href="structshark_1_1_n_s_g_a3_indicator.html#ae2a8e94c8556e915e1c7e306159a432b">leastContributors</a>(ParetofrontType <span class="keyword">const</span>&amp; front, ParetoArchive <span class="keyword">const</span>&amp; archive, std::size_t K)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="comment">//copy both fronts together into temporary.</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="comment">//remember: archived(preselected) points are at the front, points to select are at the back</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        std::vector&lt;RealVector&gt; points;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> <span class="keyword">const</span>&amp; point: archive)</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>            points.push_back(point);</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span> <span class="keyword">const</span>&amp; point: front)</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>            points.push_back(point);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        <span class="comment">//step 1: compute ideal point</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        RealVector ideal = points.front();</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span>&amp; point: points){</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>            noalias(ideal) = min(ideal,point);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        }</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="comment">//move current optimum in all objectives to 0</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span>&amp; point: points)</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            noalias(point) = point - ideal;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        RealVector normalizer = computeNormalizer(points);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="comment">//step 2.3: create normalized fitness values</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span>&amp; point: points)</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            noalias(point) = point/ normalizer;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="keyword">typedef</span> <a class="code hl_struct" href="structshark_1_1_key_value_pair.html" title="Represents a Key-Value-Pair similar std::pair which is strictly ordered by it&#39;s key.">KeyValuePair&lt;double,std::pair&lt;std::size_t, std::size_t&gt;</a> &gt; Pair;<span class="comment">//stores (dist(p_j,z_i),j,i)</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="comment">// step 3: generate associative pairings between all points and the reference points</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        std::vector&lt;Pair&gt; pairing(points.size(),<a class="code hl_function" href="namespaceshark.html#a45f02945ba29df1104c012e614d38591" title="Creates a KeyValuePair.">makeKeyValuePair</a>(std::numeric_limits&lt;double&gt;::max(),std::pair&lt;std::size_t, std::size_t&gt;()));</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="keywordflow">for</span>(std::size_t j = 0; j != points.size(); ++j){</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            <span class="comment">// find the reference this point is closest to</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>            <span class="keywordflow">for</span>(std::size_t i = 0; i != m_Z.size(); ++i){</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                <span class="comment">//by pythagoras law we have a right triangle between our point x,</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                <span class="comment">//the projection onto the line z_i = &lt;z_i,x&gt;c_i and 0.</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                <span class="comment">//therefore we have |x-&lt;z_i,x&gt;z_i|^2 = |x|^2 - &lt;z_i,x&gt;^2</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                <span class="comment">// using |z_i| = 1</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                <span class="keywordtype">double</span> dist = norm_sqr(points[j]) - <a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(inner_prod(m_Z[i],points[j]));</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                pairing[j] = min(pairing[j],<a class="code hl_function" href="namespaceshark.html#a45f02945ba29df1104c012e614d38591" title="Creates a KeyValuePair.">makeKeyValuePair</a>(dist,std::make_pair(j,i)));</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        }</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        <span class="comment">//check how points are assigned in the archive</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        std::vector&lt;std::size_t&gt; rho(m_Z.size(),0);<span class="comment">//rho_i counts the number of points assigned to Z_i</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        std::size_t k = 0;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <span class="keywordflow">for</span>(; k != archive.size(); ++k){</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            rho[pairing[k].value.second] ++;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        }</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <span class="comment">// step 4: select the points to keep</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <span class="keywordflow">while</span>(k &lt; points.size() - K){</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            <span class="comment">//find reference point that got least points assigned;</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            std::size_t index = std::min_element(rho.begin(),rho.end()) - rho.begin();</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <span class="comment">//Search for an unassigned associated point that is close to it</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="keywordtype">bool</span> found = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <a class="code hl_struct" href="structshark_1_1_key_value_pair.html" title="Represents a Key-Value-Pair similar std::pair which is strictly ordered by it&#39;s key.">KeyValuePair&lt;double,std::size_t &gt;</a> closest(std::numeric_limits&lt;double&gt;::max(),0);</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="keywordflow">for</span>(std::size_t i = k; i != points.size(); ++i){</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                <span class="keywordflow">if</span>(pairing[i].value.second == index){<span class="comment">//is this point associated?</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                    found = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>                    closest = std::min(closest,<a class="code hl_function" href="namespaceshark.html#a45f02945ba29df1104c012e614d38591" title="Creates a KeyValuePair.">makeKeyValuePair</a>(pairing[i].key,i));</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            }</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            <span class="comment">//if no point was found, we disregard the reference point from now on</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <span class="keywordflow">if</span>(!found){</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                rho[index] = points.size() +1;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>            }<span class="keywordflow">else</span>{</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                <span class="comment">//we remove it from the list of unassigned points</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                <a class="code hl_function" href="namespaceshark.html#a3fffe112e8e09ea8f41e4fb7113e93ee" title="Swaps the contents of two instances of KeyValuePair.">swap</a>(pairing[k],pairing[closest.<a class="code hl_variable" href="structshark_1_1_key_value_pair.html#a17a95cec6457d457a4c1da366fb8283f">value</a>]);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                <span class="comment">//we found a point and assign it</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                rho[index]++;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                ++k;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            }</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        }</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="comment">//return the indices of the remaining unselected points</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        std::vector&lt;std::size_t&gt; unselected;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        <span class="keywordflow">for</span>(; k != points.size(); ++k){</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(pairing[k].value.first &gt;= archive.size());</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            unselected.push_back(pairing[k].value.first - archive.size());</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        }</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="keywordflow">return</span> unselected;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        </div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>    </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Archive&gt;</div>
<div class="foldopen" id="foldopen00124" data-start="{" data-end="}">
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"><a class="line" href="structshark_1_1_n_s_g_a3_indicator.html#ab76580d0beca10b7a3df34f5895cec61">  124</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="structshark_1_1_n_s_g_a3_indicator.html#ab76580d0beca10b7a3df34f5895cec61">serialize</a>( Archive &amp; ar, <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ) {</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        ar &amp; m_Z;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    }</div>
</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    </div>
<div class="foldopen" id="foldopen00128" data-start="{" data-end="}">
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"><a class="line" href="structshark_1_1_n_s_g_a3_indicator.html#ac7b565cc0603288903fe940867016bc1">  128</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="structshark_1_1_n_s_g_a3_indicator.html#ac7b565cc0603288903fe940867016bc1">setReferencePoints</a>(std::vector&lt;RealVector&gt; <span class="keyword">const</span>&amp; Z){</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        m_Z = Z;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        </div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span>&amp; z: m_Z){</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            z /= norm_2(z);</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    }</div>
</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    </div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> random&gt;</div>
<div class="foldopen" id="foldopen00137" data-start="{" data-end="}">
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"><a class="line" href="structshark_1_1_n_s_g_a3_indicator.html#aa484bfef7ef12fa0aa42bf74238e6236">  137</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="structshark_1_1_n_s_g_a3_indicator.html#aa484bfef7ef12fa0aa42bf74238e6236">init</a>(std::size_t numOfObjectives, </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>              std::size_t mu, </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>              random&amp; rng, </div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>              std::vector&lt;Preference&gt; <span class="keyword">const</span> &amp; preferences = std::vector&lt;Preference&gt;()){</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        std::size_t numLatticeTicks = <a class="code hl_function" href="namespaceshark.html#a415796eac968fb1da2a007f6393f0eef" title="Computes the number of Ticks for a grid of a certain size.">computeOptimalLatticeTicks</a>(numOfObjectives, mu);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        RealMatrix refs;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <span class="keywordflow">if</span>(preferences.empty())</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        {</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>            refs = <a class="code hl_function" href="namespaceshark.html#a4ccee7396e4625bd05c53a87c7cd8df8">sampleLatticeUniformly</a>(</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>                rng,</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>                <a class="code hl_function" href="namespaceshark.html#af270d535e78a54515afc3761e20f61b1" title="Return a set of evenly spaced n-dimensional points on the unit sphere.">unitVectorsOnLattice</a>(numOfObjectives, numLatticeTicks),</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>                mu);</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        }</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        {</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>            refs = <a class="code hl_function" href="namespaceshark.html#ab9ca889b44ff9b2a2d1c5f362f37d72c" title="Return a set of evenly spaced n-dimensional points on the unit sphere clustered around the specified ...">preferenceAdjustedUnitVectors</a>(</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>                numOfObjectives, numLatticeTicks, preferences);</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        }</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        <span class="comment">// m_Z either has size mu or it, if preference points are given, its</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <span class="comment">// size equals the number of preference points times the number of</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        <span class="comment">// points in the lattice structure.</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        m_Z.resize(refs.size1());</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i &lt; refs.size1(); ++i){</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>            m_Z[i] = row(refs, i);</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        }</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    }</div>
</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>    std::vector&lt;RealVector&gt; m_Z;</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span> </div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <span class="comment">// approximates the points of the front by a plane spanned by the most extreme points.</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    <span class="comment">// then a normalizer is computed such that for the normalized points the plane has normal</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>    <span class="comment">// (1,1,...,1). If this fails, the normalizer is chosen such that all values lie between 0 and 1.</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>    RealVector computeNormalizer(std::vector&lt;RealVector&gt; <span class="keyword">const</span>&amp; points)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        <span class="comment">//step 1 find points spanning the plane</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordtype">double</span> epsilon = 0.00001;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        std::size_t dimensions = points.front().size();</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        RealMatrix cornerPoints(dimensions, dimensions,0.0);</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        <span class="keywordflow">for</span>(std::size_t dim = 0; dim != dimensions; ++dim){</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            <a class="code hl_struct" href="structshark_1_1_key_value_pair.html" title="Represents a Key-Value-Pair similar std::pair which is strictly ordered by it&#39;s key.">KeyValuePair&lt;double,std::size_t&gt;</a> best(std::numeric_limits&lt;double&gt;::max(),0);</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            <span class="keywordflow">for</span>(std::size_t i = 0; i != points.size(); ++i){</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>                <span class="keyword">auto</span> <span class="keyword">const</span>&amp; point = points[i];</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>                <span class="keywordtype">double</span> dist = epsilon * sum(point) + (1-epsilon) * point[dim];</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>                best = std::min(best,<a class="code hl_function" href="namespaceshark.html#a45f02945ba29df1104c012e614d38591" title="Creates a KeyValuePair.">makeKeyValuePair</a>(dist,i));</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            }</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>            noalias(row(cornerPoints,dim)) = points[best.value];</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        }</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        <span class="comment">// compute plane equation</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <span class="comment">// set up system of equations for linear regression</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <span class="comment">// the plane equation is c_i^T w + b = 0 for all</span></div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        <span class="comment">// corner points c_i. as w can be scaled freely, any value of b != 0</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        <span class="comment">// will give rise to a solution as long as the c_i are not linearly dependent.</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>        RealMatrix A = trans((cornerPoints|1)) % (cornerPoints|1);</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        RealVector b = trans((cornerPoints|1)) % blas::repeat(-1.0,dimensions);<span class="comment">//value of the right hand side of % does not matter as long as it is &lt; 0</span></div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        blas::symm_pos_semi_definite_solver&lt;RealMatrix&gt; solver(A);</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="keywordflow">if</span>(solver.rank() == dimensions){<span class="comment">//check if system is solvable</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            solver.solve(b, blas::left());</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            RealVector w = subrange(b,0,dimensions);<span class="comment">// get the plane normal.</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>            <span class="keywordflow">if</span>(min(w) &gt;= 0){<span class="comment">//check if linear factors make sense</span></div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>                <span class="keywordflow">return</span> blas::repeat(1.0,dimensions)/w;</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            }</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        }</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <span class="comment">// if some of the error conditions are true,</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        <span class="comment">// we use the worst function values as</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        <span class="comment">// normalizer</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        RealVector nadir = points.front();</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <span class="keywordflow">for</span>(<span class="keyword">auto</span>&amp; point: points){</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>            noalias(nadir) = max(nadir,point);</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        }</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        <span class="keywordflow">return</span> nadir;</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>        </div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    }</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>};</div>
</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span> </div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>}</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span> </div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span><span class="preprocessor">#endif</span></div>
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